During his speech, Michael Moore ripped up a copy of the Washington Post, saying: “The headline was ‘Trump takes power’. I don’t think so. Here’s the power. Here’s the majority of America right here. We are the majority.”

The singer Madonna also made an appearance, swearing several times in a speech carried live by major US TV networks.

“Yes, I am outraged. Yes, I have thought an awful lot about blowing up the White House,” she said.

America Ferrera told the crowd: “We march today for the moral core of this nation, against which our new president is waging a war.”

Huge crowds were reported at other US protests.

Media captionWomen’s March against Trump: What do they want?

So many turned out in Chicago – some 150,000 – that a planned march had to be called off and the event declared a rally. Streets were also overflowing in Los Angeles.

Huge crowds were also reported in New York, Seattle, Boston and Miami, some of the venues for about 300 nationwide protests.

Many women wore knitted pink “pussy hats” – a reference to a recording that emerged during the election campaign in which Mr Trump talked about groping women.

Image copyrightREUTERSImage captionWashington’s transportation system creaked under the strain of travellersImage copyrightREUTERSImage captionFormer secretary of state John Kerry joins the Washington rallyImage copyrightREUTERSImage captionA young Trump supporter gets her message across in WashingtonImage copyrightPAImage captionLondon joins in the protests that began in Australasia and have swept west to the US

‘These are global problems’

Organisers of a London rally said between 80,000 and 100,000 people had taken part there. Belfast, Cardiff, Edinburgh, Leeds, Liverpool, Manchester and Bristol were among the other UK cities holding protests.

Anti-Trump marches took place earlier in Australia, New Zealand and in several Asian cities.

Image copyrightGETTY IMAGESImage captionCrowds turned out in many European cities, including at the Brandenburg Gate in Berlin

Several thousand women and men joined a rally in central Sydney, with a similar number in Melbourne.

Women’s March Sydney co-founder Mindy Freiband told the crowd: “Hatred, hate speech, bigotry, discrimination, prejudicial policies – these are not American problems, these are global problems.”

Barcelona, Rome, Amsterdam, Geneva, Budapest, Prague and Berlin were among the European cities that took part.

In Paris, protester Francoise Seme Wallon said Mr Trump was “a nasty guy and he’s dangerous for the whole world”.